As part of a promotion a toy is put in each packet of crisps sold. There are eight different toys available. Each toy is equally likely to be found in any packet of crisps.
David buys four packets of crisps.
a. Find the probability that the four toys in these packets are all different.
b. Of the eight toys in the packets, his favourites are the yo-yo and the gyroscope. Find the probability that he finds at least one of his favourite toys in these four packets.
I'm stumped on b. Can someone explain how to do part b to me please?
Best Answer
It is easier to find first the probability that David will be sad after buying the four packets, because he only got lousy toys.
The probability a randomly selected packet contains a lousy toy is $6/8$. If we assume independence, as we are meant to do, the probability this happens $4$ times in a row is $(6/8)^4$. So the probability that at least one of the packets contains a nice toy is $1-(6/8)^4$.